An unbiased homotopy particle filter and its application to the INS/GPS integrated navigation system

A loosely coupled INS/GPS integrated navigation system is a nonlinear dynamic system. A particle filter (PF) is a particular tool for the nonlinear and non-Gaussian problems. However typical bootstrap particle filters (BPFs) cannot solve the mismatch between the importance function and the likelihood function very well so that they are invalid to some extent in the application of the INS/GPS integrated navigation systems. The homotopy particle filters (HPFs) use the corresponding homotopy transformation to replace the weights updating and the particles resampling in the BPF and then obtain significant effects. However the HPF is sensitive to the spread of the particles and its accuracy decreases with the increase of the GPS observation time intervals. Therefore we proposed a bias-correction-based HPF (BCHPF). The BCHPF firstly estimates the corresponding state bias errors according to the current observation and then corrects the bias errors of the predicted particles before implementing the homotopy transformation. Simulations and practical experiments both show that the proposed BCHPF can effectively solve the mismatch between the importance function and the likelihood function in the BPF and compensate the accumulated errors of the INSs very well. Compared with the HPF it achieves better robustness and higher accuracy.